The new data 'challenges' many old assumptions. [=the new data gives people reasons to doubt many old assumptions]
He hopes to be the governor's 'challenger' in the next election. [=the candidate running against the governor]
The coach is confident that you will 'rise to the challenge'. [=the coach is confident that you will succeed]
(..) Ho ho ho ho! You won't find him here. Ha ha. The king has returned. I can't believe it. He's gone back! Gone back? What do you mean? Hey! What's going on here? Who's the monkey?! Simba's gone to challenge Scar. Who? Scar. Who's got a scar? No, no, no. It's his uncle. The monkey's his uncle? Ohhh. (..)1994 The Lion King
(..) Ohh, I shall practice my curtsy. Don't turn your back on me, Scar. On, no, Mufasa. Perhaps you shouldn't turn your back on me. Is that a challenge? Temper, temper. I wouldn't dream of challenging you. Pity! Why not? Well, as far as brains go, I got the lion's share. (..)1994 The Lion King